Abstract
The paper considers the application of the locator cellular automaton model to the closest neighbor search problem. The locator cellular automaton model assumes the possibility for each cell to translate a signal through any distance using the ether. It was proven earlier that the ether model allows solving the problem with logarithmic time. In this paper we have derived a logarithmic lower bound for this problem.
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REFERENCES
J. von Neumann, Theory of Self-Reproducing Automata, Ed. by A. W. Burks (Univ. of Illinois Press, Urbana, Ill., 1966).
J. von Neumann, Collected Works (Pergamon Press, New York, 1961–1963).
A. Burks, Essays on Cellular Automata (Univ. of Illinois Press, Urbana, Ill., 1971).
E. F. Moore, ‘‘Machine models of self-reproduction,’’ in Mathematical Problems in the Biological Sciences (American Mathematical Society, Providence, R.I., 1962), pp. 17–34.
V. B. Kudryavtsev, A. S. Podkolzin, and A. A. Bolotov, Foundations of the Theory of Homogeneous Structures (Nauka, Moscow, 1990).
V. B. Kudryavtsev, E. E. Gasanov, and A. S. Podkolzin, Theory of Intelligent Systems, Vol. 4: Theory of Automata (Izdatel’skie Resheniya, Moscow, 2018).
E. E. Titova, ‘‘Construction of moving images by cellular automata,’’ Intellektual’nye Sist. Teoriya Prilozheniya 18 (1), 153–180 (2014).
G. V. Kalachev and E. E. Titova, ‘‘On the size of the set of motion rules realizable by cellular automata,’’ Intellektual’nye Sist. Teoriya Prilozheniya 22 (3), 105–126 (2018).
E. E. Gasanov, ‘‘Locator cellular automata,’’ Intellektual’nye Sist. Teoriya Prilozheniya 24 (2), 119–132 (2020).
D. I. Vasil’ev, ‘‘The closest neighbour problem solution using the locator cellular automaton model,’’ Intellektual’nye Sist. Teoriya Prilozheniya 24 (3), 99–119 (2020).
D. I. Vasil’ev, ‘‘The closest neighbour problem on a plane solution using the locator cellular automaton model,’’ Intellektual’nye Sist. Teoriya Prilozheniya 25 (4), 83–87 (2021).
G. V. Kalachev, ‘‘Remarks on the definition of locator cellular automaton,’’ Intellektual’nye Sist. Teoriya Prilozheniya 24 (4), 47–56 (2020).
D. E. Ibragimova, ‘‘The addition of vectors problem solution using the locator cellular automaton,’’ Intellektual’nye Sist. Teoriya Prilozheniya 26 (4), 134–162 (2022).
ACKNOWLEDGMENTS
The authors thank Candidate of Physical and Mathematical Sciences G.V. Kalachev for fruitful remarks.
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This work was supported by ongoing institutional funding. No additional grants to carry out or direct this particular research were obtained.
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Translated by E. Oborin
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Vasilev, D.I., Gasanov, E.E. A Lower Bound on Complexity of a Locator Cellular Automaton Solution for the Closest Neighbor Search Problem. Moscow Univ. Math. Bull. 78, 244–252 (2023). https://doi.org/10.3103/S0027132223050078
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DOI: https://doi.org/10.3103/S0027132223050078